Density-dependent incompressible Navier--Stokes equations in critical tent spaces

2023/05/15 by Raphaël Danchin, Ioann Vasilyev, Danchin, Raphaël +1
#math.AP

paper · pdf · doi:10.48550/arxiv.2305.09027

Abstract

In this article, we prove the existence of global solutions to the inhomogeneous incompressible Navier--Stokes equations, whenever the initial velocity belongs to a certain subspace of BMO^-1, and the initial density is sufficiently close to 1 in the uniform metric. This is a natural extension to the variable density case of the celebrated result by H. Koch and D. Tataru concerning the classical Navier-Stokes equations.

Citations

• Some new function spaces and their applications to Harmonic analysis
• Sur le mouvement d'un liquide visqueux emplissant l'espace

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